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We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of…

Dynamic graph augmentation is used to improve the performance of dynamic GNNs. Most methods assume temporal locality, meaning that recent edges are more influential than earlier edges. However, for temporal changes in edges caused by random…

Robotic manipulation in dynamic environments often requires seamless transitions between different grasp types to maintain stability and efficiency. However, achieving smooth and adaptive grasp transitions remains a challenge, particularly…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…

Two-sample multiple testing problems of sparse spatial data are frequently arising in a variety of scientific applications. In this article, we develop a novel neighborhood-assisted and posterior-adjusted (NAPA) approach to incorporate both…

The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…

Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. However, their predictions are often not interpretable. Post-hoc instance-level explanation methods have been proposed…

We propose shifted inner-product similarity (SIPS), which is a novel yet very simple extension of the ordinary inner-product similarity (IPS) for neural-network based graph embedding (GE). In contrast to IPS, that is limited to…

Graph anomaly detection technology has broad applications in financial fraud and risk control. However, existing graph anomaly detection methods often face significant challenges when dealing with complex and variable abnormal patterns, as…

The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…

We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…

This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) time-marching methods to the generalized summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods are shown to retain: A and…

This paper aims to simulate viscoplastic flow in a shallow-water regime. We specifically use the Bingham model in which the material behaves as a solid if the stress is below a certain threshold, otherwise, it moves as a fluid. The main…

Graph invariant learning (GIL) seeks invariant relations between graphs and labels under distribution shifts. Recent works try to extract an invariant subgraph to improve out-of-distribution (OOD) generalization, yet existing approaches…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods,…